water
Article
Integrated Modeling of Hybrid Nanofiltration/Reverse Osmosis
Desalination Plant Using Deep Learning-Based Crow Search
Optimization Algorithm
Sani. I. Abba 1 , Jamilu Usman 1, * , Ismail Abdulazeez 1 , Dahiru U. Lawal 1, * , Nadeem Baig 1 ,
A. G. Usman 2 and Isam H. Aljundi 1,3
1
2
3
*
Citation: Abba, S.I.; Usman, J.;
Abdulazeez, I.; Lawal, D.U.; Baig, N.;
Usman, A.G.; Aljundi, I.H. Integrated
Modeling of Hybrid Nanofiltration/
Reverse Osmosis Desalination Plant
Using Deep Learning-Based Crow
Search Optimization Algorithm.
Water 2023, 15, 3515. https://
doi.org/10.3390/w15193515
Interdisciplinary Research Centre for Membrane and Water Security, King Fahd University of Petroleum and
Minerals, Dhahran 31261, Saudi Arabia; sani.abba@kfupm.edu.sa (S.I.A.);
ismail.abdulazeez@kfupm.edu.sa (I.A.); nadeembaig@kfupm.edu.sa (N.B.); aljundi@kfupm.edu.sa (I.H.A.)
Operational Research Centre in Healthcare, Near East University, TRNC, Mersin 10, Nicosia 99138, Turkey;
abdullahigusman@gmail.com
Department of Chemical Engineering, King Fahd University of Petroleum and Minerals,
Dhahran 31261, Saudi Arabia
Correspondence: jamilu.usman@kfupm.edu.sa (J.U.); dahiru.lawal@kfupm.edu.sa (D.U.L.)
Abstract: The need for reliable, state-of-the-art environmental investigations and pioneering approaches to address pressing ecological dilemmas and to nurture the sustainable development goals
(SDGs) cannot be overstated. With the power to revolutionize desalination processes, artificial intelligence (AI) models hold the potential to address global water scarcity challenges and contribute to a
more sustainable and resilient future. The realm of desalination has exhibited a mounting inclination
toward modeling the efficacy of the hybrid nanofiltration/reverse osmosis (NF–RO) process. In this
research, the performance of NF–RO based on permeate conductivity was developed using deep
learning long short-term memory (LSTM) integrated with an optimized metaheuristic crow search
algorithm (CSA) (LSTM-CSA). Before model development, an uncertainty Monte Carlo simulation
was adopted to evaluate the uncertainty attributed to the prediction. The results based on several
performance statistical criteria (root mean square error (RMSE) and mean absolute error (MAE))
demonstrated the reliability of both LSTM (RMSE = 0.1971, MAE = 0.2022) and the LSTM-CSA
(RMSE = 0.1890, MAE = 0.1420), with the latter achieving the highest accuracy. The accuracy was also
evaluated using new 2D graphical visualization, including a cumulative distribution function (CDF)
and fan plot to justify the other evaluation indicators such as standard deviation and determination
coefficients. The outcomes proved that AI could optimize energy usage, identify energy-saving opportunities, and suggest more sustainable operating strategies. Additionally, AI can aid in developing
advanced brine treatment techniques, facilitating the extraction of valuable resources from the brine,
thus minimizing waste and maximizing resource utilization.
Academic Editor: Anshul Yadav
Received: 1 September 2023
Keywords: desalination; machine learning; uncertainty; permeate conductivity; deep learning
Revised: 28 September 2023
Accepted: 4 October 2023
Published: 9 October 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
1. Introduction
The rising demand for freshwater, stemming from burgeoning population numbers,
expansive industrial endeavors, and rapid urban growth, has driven us into a global water
sustainability crisis [1,2]. This crisis manifests in several ways: deteriorating freshwater
resources due to over-exploitation of surface waters and groundwater reserves, protracted
periods of drought impaired by climate shifts, the encroachment of seawater into freshwater
reserves, accelerated depletion of groundwater levels, and increased salinization and
contamination of our freshwater bodies. Such precarious circumstances jeopardize both
national and global water security [3]. As a response to these pressing challenges, the
world is increasingly turning to the desalination of brackish water and saltwater as primary
Water 2023, 15, 3515. https://doi.org/10.3390/w15193515
https://www.mdpi.com/journal/water
Water 2023, 15, 3515
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sources of a dependable water supply [4]. This process involves the extraction of salt
from water, making it suitable for diverse uses such as agricultural irrigation, industrial
processes, and daily household needs [5,6]. Highlighting the immense promise of this
technique, the United Nations put forward that saltwater desalination can augment our
water reserves beyond what the natural hydrological cycle can offer.
Addressing the escalating need for freshwater, the primary strategies being adopted
are desalination through thermal methods and membrane-based separation techniques [5].
Digging deeper into these methods, two prominent processes emerge: reverse osmosis
(RO)—a membrane-based technology, and multistage flash distillation (MSF)—a heatdriven purification approach [7]. Thermal desalination, primarily using the MSF method,
is frequently lauded for its efficiency, particularly when handling water with a high salt
concentration. The resulting water or ‘permeate’ from this method is of superior quality [4].
On the other hand, the global desalination landscape is dominated by the RO system, with
a staggering 90% of facilities around the world harnessing this technique. The RO method
leverages semi-permeable membranes to sieve out salts and other unwanted minerals from
water [8]. Its popularity is not unwarranted; RO is recognized for its economical nature,
impressive salt rejection rates, and the high quality of the resultant water. Its adaptability is
another selling point—RO systems have found homes in diverse environments, ranging
from standard water and sewage treatment plants to cutting-edge wastewater recovery
and reuse initiatives. Nonetheless, the RO method is not without its challenges. Factors
such as the requirement for high feed pressures; considerable energy and cost expenditures;
the need for periodic membrane maintenance; and fluctuations in temperature, energy,
and costs depending on the time of day or season, continually push researchers and
technologists to innovate and improve RO systems [7].
Membrane fouling has long been identified as one of the fundamental challenges
associated with the RO desalination technique. However, recent studies suggest that
this problem can be considerably mitigated, if not wholly resolved, by integrating the
RO process with nanofiltration (NF), especially in the realm of seawater desalination.
The incorporation of NF into RO systems substantially enhances the efficiency of the
desalination process by actively reducing the presence of organics, pollutants, and ionic
strength, and by softening the water. This combined approach also leads to a notable
decrease in the overall expenditure tied to desalination [9,10]. The appeal of NF extends
beyond its capacity to complement RO. Researchers laud its multiple benefits, such as
cost-effective operation and maintenance, impressive water throughput (flux), operation at
reduced pressures, and its relatively low installation expenses [10]. That said, a singular
reliance on NF is not without its drawbacks. While it can treat various water impurities
effectively, NF in isolation falls short in adequately reducing the high salinity inherent
in seawater to produce potable water. This shortcoming is where the combined might of
NF and RO shines through, achieving better desalination results [11]. Emerging research
in the realm of membrane technologies, be it NF, RO, or innovative hybrid separation
processes, consistently underscores that energy consumption stands as the most daunting
challenge in their operational spectrum. It is evident that the desalination processes are
composed of multifaceted components like permeate rate, conductivity, recovery, rejection
rate (RR), permeate quality (PQ), pH (potential hydrogen) levels, energy consumption, and
associated costs. In a pursuit to optimize these factors, various experimental undertakings
have advocated for blended solutions, such as the NF–RO combination and the NF–SWRO–
MSF hybrid process. In these innovative configurations, NF primarily functions as an
efficient pre-treatment stage, preparing the ground for the more intensive RO desalination
process [12,13].
Generally, membrane processes in desalination have predominantly been based on
linear or polynomial correlations, even though these methods may generalize the complex
dynamics of the desalination procedure [14–16]. In contrast to these mathematical and
traditional paradigms, which often settle for lower precision, the modern technological
landscape, marked by the beginning of Industry 4.0 and the growing field of the Industrial
Water 2023, 15, 3515
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Internet of Things (IoT), has seen artificial intelligence (AI) algorithms making substantial
inroads into various industrial spheres [17]. Rather than the novel computing methodologies which prioritize absolute accuracy and unerring truth, the world of soft computing
embraces the nuances of imprecision, accepts degrees of truth, grapples with uncertainty,
and is amenable to approximations in order to accomplish a specific objective [18–20].
This adaptive approach has been validated using cutting-edge studies, which reveal that
sophisticated intelligent systems possess the prowess to assimilate experimental data with
impeccable accuracy in the realm of desalination [4,21–25]. Nevertheless, the journey of
integrating data-driven algorithms into the ecosystem of desalination processes, including
RO and NF, has not been devoid of hurdles. Artificial Neural Networks (ANNs), although
revolutionary, have come under scrutiny for certain limitations: their propensity for overfitting, challenges with plant-specific performance optimization, the intricacies of their
internal tuning parameters, and concerns over data homogeneity and inadequate neuron
configurations [26].
Achite et al. [27] introduced a hybrid model known as the M5-Gorilla Troops Optimizer
(GTO), built upon a blend of the M5 and GTO algorithms. This research employed nine
diverse parameters including raw water production (RWP), water turbidity, conductivity,
TDS, salinity, pH, water temperature (WT), SM, and O2 as inputs for CD modeling. The
comparative analysis highlighted in the study robustly positions the M5-GTO model as
superior in CD modeling accuracy against numerous established models such as multiple
linear and nonlinear regression, an artificial neural network, multivariate adaptive regression splines, an M5 model tree, k-nearest neighbor, a least-squares support vector machine,
a general regression neural network, and random forest (RF). This was exemplified by
the recorded values of various error metrics and correlation coefficient criteria for the
M5-GTO, all demonstrating significant improvements over the least effective algorithm, the
LSSVM. The findings further ranked M5 and RF algorithms second and third, respectively.
Moreover, the research provided insight into the significant impact of RWP and WT on CD
alterations, showcasing the inverse relationship of RWP with CD and the direct relation of
WT with CD. In the study conducted by Firzin et al. [28], a novel BLSTM-HHO algorithm
was introduced for an improved groundwater table (GWT) and drought predictions. This
innovative algorithm notably outperformed other benchmark algorithms such as the standalone BLSTM, LSTM, ANN, SARIMA, and ARIMA in terms of prediction accuracy and
performance criteria. Similarly, in the research conducted by Yan et al. [29] an innovative
approach to predicting influent ammonia nitrogen (NH3-N) concentration in wastewater treatment plants was proposed, leveraging the synergistic capabilities of the rolling
decomposition method and deep learning algorithms. The integrated model delineated
in the study notably circumvents information leakage during the decomposition process,
showcasing enhanced performance compared to standalone GRU models as evidenced by
reduced RMSE, MAE, and MAPE values. The study robustly underscores the superiority of
the proposed model over other integrated models trained with information leakage, highlighting notable strides in prediction accuracy. Recognizing these challenges, the scientific
community has proposed an advanced model called the long short-term memory (LSTM)
model. This model is further strengthened by integrating a powerful metaheuristic optimization algorithm—the crow search algorithm (CSA)—promising enhanced performance
and adaptability in desalination processes.
In an effort to handle challenges faced in the field of desalination modeling, we sought
to leverage the advanced capabilities of the LSTM network. The primary focus of this
study was to refine the model’s performance, particularly for the uncertainty analysis and
prediction of the hybrid NF–RO desalination process. To realize this aim, we employed a
state-of-the-art metaheuristic optimization technique, the CSA. A noteworthy novelty of our
methodology was the inclusion of the Particle Swarm Optimization (PSO) algorithm. This
algorithm was instrumental in recognizing the optimal combination of features, serving
as a foundation to our in-depth modeling, statistical evaluations, and graphical analysis.
Such a strategic approach was intended to maximize the accuracy of the hybrid algorithms
Water 2023, 15, 3515
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(LSTM-CSA) as well as the LSTM in its single form. For modeling purposes, the six most
important parameters were accurately sourced from seventy-three distinct data points. The
chosen independent parameters covered a diverse range: temperature (◦ C), time duration
(h), pressure levels (kg/cm2 ), feed flow rate (m3 /h), and feed conductivity (µs/cm). On the
other hand, our target or dependent parameter was identified as the permeate conductivity
(µS/cm). Through the feature selection insights collected from the PSO algorithm, two
distinct datasets were crafted. The result of our study is expected to show a comprehensive
evaluation of these models, with both training and testing datasets subjected to performance
metrics like the root mean square error (RMSE) and the mean absolute error (MAE). The
finding was that explaining models powered by the metaheuristic algorithms notably
outperformed the singular LSTM model in terms of accuracy.
It is worth mentioning that the use of deep learning in the desalination process, as
illustrated in the given abstract and introduction, holds significant promise in revolutionizing the efficacy and sustainability of water desalination [6,30–32]. The application of LSTM
networks integrated with an optimized metaheuristic CSA in the hybrid NF–RO desalination process enhances the overall performance, offering notable advantages. One of the
primary benefits is the increased accuracy in predicting the desalination process outcomes,
with substantial reductions in root mean square error (RMSE) and mean absolute error
(MAE), demonstrating the reliability of AI models. This integration also optimizes energy
usage, enabling the identification and exploitation of energy-saving opportunities for more
sustainable operation. Additionally, AI contributes to the development of advanced brine
treatment techniques, minimizing waste and maximizing resource utilization by facilitating
the extraction of valuable resources from the brine. The models accurately evaluate and
mitigate the uncertainty associated with predictions, ensuring more consistent and reliable
desalination results. The comprehensive optimization of various desalination factors, including permeate rate and conductivity, underscores the significant enhancement AI brings
to water treatment and desalination, addressing and overcoming many challenges inherent
in traditional methods [33–35].
The goals and objectives of this research are primarily centered around tackling global
water scarcity by enhancing desalination processes, specifically focusing on the hybrid
NF–RO process. This research aims to develop a model for evaluating the performance of
NF–RO based on permeate conductivity, utilizing deep LSTM integrated with an optimized
metaheuristic CSA and LSTM-CSA. By adopting uncertainty Monte Carlo simulation, this
study evaluates the uncertainty attributed to prediction, aiming to prove the reliability of
both LSTM and the LSTM-CSA in terms of various performance statistical criteria. This
research further addresses the key challenges faced in the RO desalination technique,
aiming to enhance its efficiency by integrating it with NF, and subsequently optimizing
various parameters involved in desalination processes. This study also seeks to leverage the
advanced capabilities of the LSTM network and the CSA to refine the model’s performance,
particularly for the uncertainty analysis and prediction of the hybrid NF–RO desalination
process. This paper is committed to maximizing the accuracy of the hybrid algorithms and
providing a comprehensive evaluation, contributing to the optimization of energy usage,
identification of energy-saving opportunities, and the development of more sustainable
operating strategies in desalination processes.
2. Experimental Methods
In this study, we aimed to model a complex hydro-environmental system using six
parameters, which were sampled at seventy-three different points. The independent
variables consisted of temperature (◦ C), time (h), pressure (kg/cm2 ), flow feed (m3 /h), and
conductivity feed (µS/cm), while the dependent variable was permeating conductivity (PC)
(µS/cm). The data were obtained from the Saline Water Desalination Research Institute
(SWDRI) of the Saline Water Conversion Corporation (SWCC), Saudi Arabia [36], and
open-source data were collected from [8]. Refer to [36] for details of the experimental
analysis and set-up discussion; the diagram is presented in Figure 1a. An essential stage in
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open-source data were collected from [8]. Refer to [36] for details of the experimental analysis and set-up discussion; the diagram is presented in Figure 1a. An essential stage in
developing deep learning models is the processing of gathered data and the selection of
developing
deep combination.
learning models
the processing
of gathered
datacan
andbe
thetackled
selection
the
the right model
Theisintricacy
of these
built models
by of
emright
model
combination.
The
intricacy
of
these
built
models
can
be
tackled
by
employing
ploying a multiple heuristic approach such as the CSA and understanding the extent of
aAI
multiple
approach
such
the CSA and understanding
the extent of AI systems
systemsheuristic
to manage
complex
andasnonlinear-system-like
desalination.
to manage complex and nonlinear-system-like desalination.
Figure 1. (a) Experimental pilot-plant setup; (b) uncertainty analysis; (c) PSO algorithms.
Figure 1. (a) Experimental pilot-plant setup; (b) uncertainty analysis; (c) PSO algorithms.
In this work, we employed a Monte Carlo simulation (Figure 1b) to investigate the unIn this
we metaheuristic
employed a Monte
Carlowas
simulation
(Figure
to investigate
the1c
certainty,
andwork,
the PSO
algorithm
used to solve
this1b)
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In Figure
uncertainty,
and
the
PSO
metaheuristic
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was
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to
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problem.
In
is the objective function for selecting optimal features using the PSO algorithm. Further
Fiugure 1c is the
objective
function for
features
using
the PSO was
algorithm.
pre-processing
using
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to selecting
improve optimal
the accuracy
of the
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carried
Further
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out. The model development also takes into consideration 5k-fold cross-validation towas
procarried
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takesthe
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vide
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model
performs5k-fold
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provide
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intoahow
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performs across
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Thea5k-fold
cross-validation
provides
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of howdifferent
a model
subsets
of
data.
The
5k-fold
cross-validation
provides
a
more
reliable
assessment
of how
will perform on unseen data by using different data subsets for training and validation
[37].
will
perform
unseen
data by usingand
different
subsets for training
andof
Ita ismodel
widely
used
in ML on
to tune
hyperparameters
assess data
the generalization
capability
models. Figure 2 presents the descriptive statistics for visualization that provide a summary
of the main aspects of the data, offering a snapshot of their main characteristics [37]. It is
often the first step in data analysis, simplifying large amounts of data in a sensible way.
In the scenario described in Figure 2a indicating the temperature in an NF/RO system
Water 2023, 15, 3515
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to show a sharp drop, several factors could be responsible, and it is crucial to examine
the experimental setup and conditions to determine the exact cause. It might be related
to an experimental error, where an issue with the equipment, such as a malfunctioning
temperature sensor, could give inaccurate readings. Another possibility could be a sudden
change in the system parameters or operating conditions, such as a sudden influx of feed
water at a different temperature or a change in the ambient conditions. An unexpected
drop in temperature could also relate to the system’s performance, indicating potential
issues or inefficiencies within the NF–RO process itself, such as unexpected heat loss. It is
crucial to thoroughly investigate the system, review the experimental procedure, and check
the equipment to accurately diagnose the reason behind the sudden temperature drop.
In this paper, deep learning and CSA are applied to improve the performance and
efficiency of hybrid NF–RO desalination processes. Specifically, a LSTM network, a type of
recurrent neural network, is used to model the desalination process. The LSTM network is
adept at learning from sequences of data, which makes it suitable for modeling complex
processes such as desalination where numerous variables interact over time. LSTM is
integrated with the CSA, a metaheuristic optimization algorithm. The CSA is inspired
by the behavior of crows and is used to optimize the parameters of the LSTM network,
ensuring that the model makes the most accurate predictions possible. Before developing
this LSTM-CSA model, an uncertainty analysis is conducted using a Monte Carlo simulation
to evaluate potential uncertainties related to the predictions made by the model. This
innovative approach utilizing both LSTM and CSA is designed to enhance the prediction of
the performance of the NF–RO desalination process based on permeate conductivity, a key
parameter in assessing the effectiveness of the desalination process. This research aims to
optimize energy usage and suggest more sustainable operating strategies for desalination,
ultimately leading to enhanced water recovery rates, reduced energy consumption, and
improved overall efficiency of the desalination process. In a more technical understanding,
the LSTM network is trained using historical data from the desalination process, learning to
identify patterns and relationships that are not easily discernible. It then uses this learning
to make predictions about the performance of the desalination process under various
conditions. The CSA is applied to fine-tune the parameters of the LSTM network, ensuring
that it operates as effectively as possible. The integration of deep learning with the CSA
thus presents a robust and innovative approach to optimizing the performance of NF–RO
desalination processes, contributing to advancements in addressing global water scarcity
challenges. The performance criteria used to calculate the models’ accuracy are presented
in the following equations [38,39]:
r
RMSE =
MAE =
MSE =
2
1 N Y
−
Y
( p)
(o )
N ∑ i =1
∑iN=1 y( p) − y(o)
N
∑iN=1 Y( p) − Y(o)
N
(1)
(2)
2
(3)
where Y pre, i Ycom,i Ypre and Ycom indicate the predicted and computed values Y, with N as
the means for the data points.
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2. Input-output
visualization
in terms
of (a)
embedded
responseplot
plot and
and (b)
Figure Figure
2. Input-output
visualization
in terms
of (a)
embedded
response
(b) box
boxplot
plotshowing
showing
the
outliers
and
basic
descriptive
statistic.
the
outliers
and
basic
descriptive
statistic.
2.1. Long-Term
Memory
Network
2.1. Long-Term
Memory
Neural Neural
Network
(LSTM)(LSTM)
The LSTM
network
emerges
as an advanced
variation
of the recurrent
The LSTM
neural neural
network
emerges
as an advanced
variation
of the recurrent
neural neural
network
(RNN).
Its
inception
was
specifically
aimed
at
addressing
the
inherent
network (RNN). Its inception was specifically aimed at addressing the inherent shortcom- shortof traditional
RNNs, especially
theirtoinability
to retainover
memory
over seextended
ings ofcomings
traditional
RNNs, especially
their inability
retain memory
extended
sequences
(see
Figure
3).
A
significant
triumph
of
LSTM
over
its
predecessor
is
its
prowess
quences (see Figure 3). A significant triumph of LSTM over its predecessor is its prowess
in resolving issues tied to vanishing and exploding gradients, which historically plagued
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in resolving issues tied to vanishing and exploding gradients, which historically plagued
8 of 17
the training of RNNs. This enhanced capability not only rectifies these problems but also
augments the accuracy of models based on recurrent networks—a notable advancement
as reported in the literature [40]. Diving deeper into their structure, LSTM neural netthe training of RNNs. This enhanced capability not only rectifies these problems but also
works introduce a set of intricate memory cells. Unlike the transient memory of convenaugments the accuracy of models based on recurrent networks—a notable advancement as
tional RNNs, these memory cells exhibit a longer retention span. The configuration of
reported in the literature [40]. Diving deeper into their structure, LSTM neural networks
these cells can be visualized as interconnected chains, echoing the modular repetition in
introduce a set of intricate memory cells. Unlike the transient memory of conventional
conventional RNNs. In their research, Li et al. [41] emphasized the unique structure of
RNNs, these memory cells exhibit a longer retention span. The configuration of these cells
these repeating units. LSTM neural networks boast a range of specialized components,
can be visualized as interconnected chains, echoing the modular repetition in conventional
each designed meticulously to process and hold onto extensive sequences. These compoRNNs. In their research, Li et al. [41] emphasized the unique structure of these repeating
nents not only ensure that information is accurately captured but also make it possible for
units. LSTM neural networks boast a range of specialized components, each designed
the
network to decide
whatand
to remember
and what to
discard, granting
LSTM neural
meticulously
to process
hold onto extensive
sequences.
These components
notnetonly
works
their
signature
ability
to
remember
sequences
over
a
protracted
period.
ensure that information is accurately captured but also make it possible for the network
At the heart
LSTM structure
lies
memory
cell, anLSTM
intricate
assembly
pivotal
to decide
whatof
tothe
remember
and what
tothe
discard,
granting
neural
networks
their
tosignature
the LSTMability
neuraltonetwork’s
prowess.
This
memory
cell
is
crafted
as
a
network
of sigremember sequences over a protracted period.
moid neurons
interconnected
instructure
a mannerlies
that
a unique
self-feedback
loop. Such
a
At the heart
of the LSTM
theoffers
memory
cell, an
intricate assembly
pivotal
configuration
thenetwork’s
memory cell
to fine-tune
operations,
choosing
whatof
to the LSTMallows
neural
prowess.
Thisits
memory
cell selectively
is crafted as
a network
information
to
retain
and
what
to
dispose
of
over
prolonged
durations.
Aside
from
the a
sigmoid neurons interconnected in a manner that offers a unique self-feedback loop. Such
memory
cell
and
hidden
state,
LSTM
neural
networks
have
three
specialized
gates,
each
configuration allows the memory cell to fine-tune its operations, selectively choosing what
serving
a distinct
purpose.
research
of Zaytar
El Amranidurations.
[42] emphasized
the esinformation
to retain
andThe
what
to dispose
of over&prolonged
Aside from
the
sence
of
these
gating
mechanisms.
Their
ability
to
judiciously
regulate
the
influx
and
efmemory cell and hidden state, LSTM neural networks have three specialized gates, each
flux
of information
renders The
the LSTM
neural
network
its unique
to the
maintain
serving
a distinct purpose.
research
of Zaytar
& El Amrani
[42]capability
emphasized
essence
relevant
data
and mechanisms.
discard the superfluous,
ensuring
optimum
performance
over
extended
of these
gating
Their ability
to judiciously
regulate
the influx
and
efflux of
sequences.
information renders the LSTM neural network its unique capability to maintain relevant
data and discard the superfluous, ensuring optimum performance over extended sequences.
Figure
The
LSTM
neural
network
general
architecture.
Figure
3. 3.
The
LSTM
neural
network
general
architecture.
2.2.
Crow
Search
Algorithm
(CSA)
2.2.
Crow
Search
Algorithm
(CSA)
The
CSA
optimization
algorithm
inspired
the
social
behavior
and
memory
The
CSA
is is
anan
optimization
algorithm
inspired
byby
the
social
behavior
and
memory
capability of crows, specifically their ability to hide food and remember its location for
capability of crows, specifically their ability to hide food and remember its location for
future use. This nature-inspired heuristic approach is relatively new compared to other
future use. This nature-inspired heuristic approach is relatively new compared to other
swarm intelligence techniques, yet it has been shown to have competitive performance
swarm intelligence techniques, yet it has been shown to have competitive performance for
for certain optimization problems [43,44]. The program emulates the crow’s behavior by
certain optimization problems [43,44]. The program emulates the crow’s behavior by
dividing the search space into various sub-regions, each symbolizing a potential food
source. It then modulates the positions of these sub-regions, drawing parallels to how
crows hide and recover food. Within the CSA algorithm, a collective optimization method,
agents are employed where each one represents a crow, facilitating the exploration of the
Water 2023, 15, 3515
dividing the search space into various sub-regions, each symbolizing a potential food
source. It then modulates the positions of these sub-regions, drawing parallels to how
9 of 17
crows hide and recover food. Within the CSA algorithm, a collective optimization method,
agents are employed where each one represents a crow, facilitating the exploration of the
search area. These agents collaborate, sharing insights about the most promising food
sources
identified
soagents
far. In this
distance-centric
method,
in closer
search area.
These
collaborate,
sharing communication
insights about the
most agents
promising
food
proximity
exchange
informationcommunication
compared to those
positioned
farther
sources identified
somore
far. Inextensive
this distance-centric
method,
agents in
closer
away
[44]. exchange more extensive information compared to those positioned farther
proximity
In[44].
addition to its exploration prowess, the CSA incorporates an exploitation strategy
away
that homes
in on to
pinpointing
the optimal
solution.
mechanism
the positions
In addition
its exploration
prowess,
the CSAThis
incorporates
anadjusts
exploitation
strategy
that
homes
in on pinpointing
optimal solution.
This identified
mechanismthus
adjusts
of
of
agents
relative
to the mostthe
promising
food source
far. the
Thepositions
CSA has
agents relativeits
to efficacy
the mostin
promising
food source identified
thus
Thelike
CSAengineering
has demondemonstrated
solving optimization
challenges
in far.
fields
strated its
efficacy
in solving
challenges
in fields like
engineering
design,
design,
feature
selection,
andoptimization
image processing.
Furthermore,
Figure
4 presents
a
feature selection,
and image
processing.
Furthermore,
Figure 4 presents
a comprehensive
comprehensive
flowchart
detailing
the CSA’s
process, highlighting
its primary
stages. The
flowchart
detailing
the CSA’srandomly
process, highlighting
its primary stages.
swarm
of crows
is initialized
within a d-dimensional
space.The
Theswarm
fitness of
ofcrows
each
is initialized
randomly
a d-dimensional
space.
The fitness
of evaluation,
each crow isan
assessed
crow
is assessed
using awithin
specific
fitness function,
and based
on this
initial
using a specific
function,
based
onits
this
evaluation,
anininitial
memoryvariable,
value is
memory
value isfitness
assigned.
Everyand
crow
saves
hiding
location
its memory
assigned.
Every
crow
saves
its
hiding
location
in
its
memory
variable,
denoted
as
mi. as
To
denoted as mi. To update its position, a crow selects another random crow, represented
update
its in
position,
a crow selects
anothervalue.
random
crow,value
represented
as xj,
which
in turn
xj,
which
turn produces
a random
If this
surpasses
the
awareness
produces a threshold
random value.
If this
value
surpasses
probability
threshold ‘AP’,
probability
‘AP’, the
crow
xi will
track xjthe
toawareness
pinpoint the
location mj.
the crow xi will track xj to pinpoint the location mj.
Figure4.4.Exploitation
Exploitationand
andexploration
explorationof
ofCSA
CSAmodel
model(a)
(a)f1
f1<<1,1,(b)
(b)f1f1>>11.
Figure
3. Results
3. Results
In recent times, the convergence of the Industrial Revolution 4.0 with the adoption of
In recent
times,Intelligence
the convergence
of the
Industrial
Revolution
4.0 with thehas
adoption
emerging
Artificial
(AI) and
Internet
of Things
(IoT) technologies
markedofa
emerging
Artificial
Intelligence
(AI)
and
Internet
of
Things
(IoT)
technologies
has
marked
significant advancement in the fields of wastewater treatment and desalination plants.
This
arevolution
significantrepresents
advancement
in theoffields
of aimed
wastewater
treatment
and desalination
plants.
the peak
efforts
at effectively
harnessing
these advanced
This
revolution
the peak
of management
efforts aimedchallenges.
at effectively
harnessing
these adtechnologies
to represents
address crucial
water
Within
this context,
the
vanced
technologies
to
address
crucial
water
management
challenges.
Within
this
context,
integration of ML techniques into the operational framework of desalination processes has
the
integration
of MLattention.
techniques
intointegration
the operational
framework
of desalination
gained
substantial
This
is seen
as a pivotal
approach toprocesses
optimize
has
gained
substantial
attention.
This
integration
is
seen
as
a
pivotal
approach
to optimize
and precisely control various aspects of the desalination process. Previous studies
have
and
precisely
control the
various
aspects
the desalination
process.
studiesin
have
already
underscored
potential
andoffeasibility
of employing
MLPrevious
methodologies
this
domain. In this section, we employed the novel deep learning-based LSTM algorithm and
CSA as evolutionary optimization data-driven techniques to simulate the PC (µS/cm) in
a desalination plant. As mentioned above, a stationary analysis was carried out through
the application of Augmented Dickey–Fuller (ADF) and Phillips–Perron (PP) tests. This
approach was adopted to address the nonstationary nature of each individual input as
Water 2023, 15, 3515
10 of 17
well as the independent and dependent variables. Although this sort of data mining
and enhancement is not a conventional procedure in advanced engineering problems
like desalination plants, its significance has been highlighted and recognized as a critical
stage in the field of data analysis. The result for the training phase based on several
performance indicators is presented in Table 1. Prior to model development, appropriate
feature engineering owing to the complexity of the system was conducted using GA
algorithms. Hence, the GA used a robust nonlinear input feature selection approach.
The GA was developed in MATLAB 2022b to select the best optimal objective function
for model development. The GA feature can help researchers select the most important
input variables for modeling and predicting the PC of a complex environmental system.
Table 1 shows the indicators based on MAE, MSE, and RMSE, which help to evaluate the
accuracy and reliability of the predicted models. It is worth noting that the deep learning
LSTM model is a type of recurrent neural network (RNN) commonly used for sequence
prediction tasks, such as time series data like PC in this case. For this purpose, modeling
was performed using three LSTM, LSTM-GA, and LSTM-CSA algorithms. Python language
was used for all implementations on a PC with a 3 GHz Core i7 processor and 64 GB of
RAM. The lower the MSE, the closer the predicted values are to the actual values. In
this case, LSTM-CSA-M2 has the lowest MSE (0.1447), indicating that it has the best
overall predictive accuracy among the four models. Similar to MSE, lower RMSE values
suggest better predictive performance. Here, the LSTM-CSA-M2 again has the lowest
RMSE, indicating that it makes predictions with the smallest average error magnitude.
It can be seen that metaheuristic optimization techniques are primarily used for solving
optimization problems. It is well-suited for problems where finding the optimal solution
is challenging due to complex, non-linear, and multi-dimensional search spaces; hence,
its superiority is not surprising. It is well known that the choice between the CSA and
the LSTM model depends on your specific problem domain, the nature of your data, and
your goals. If your goal is to optimize parameters or find optimal solutions in complex
spaces, the CSA might be more suitable. On the other hand, if the problem is to capture
the temporal patterns, the LSTM model could be the better choice. Figure 5 presents the
probability cumulative distribution function between the observed and simulated variables.
In the analysis regarding NF–RO desalination utilizing LSTM and LSTM-CSA models,
it is vital to precisely assess potential errors and experiment shortcomings. Uncertainty
analysis, performed using a Monte Carlo simulation prior to model development, should be
critically evaluated for comprehensive and accurate execution using various error criteria.
The integration of LSTM with the CSA requires precise tuning; any integration issues could
negatively affect the results, leading to inaccuracies in permeate conductivity predictions.
This research’s reliance on diverse parameters for modeling introduces the possibility
of another potential error. Accurate and consistent measurements are fundamental to
ensure the reliability of model predictions. Concerning the observed temperature drop
(Figure 2a) in the NF–RO system, a thorough investigation is necessary to determine if
it is an experimental error, a system issue, or a valid result. Comprehensive analysis,
considering all potential errors, is crucial for validating the research findings and their
real-world applicability in desalination processes.
Table 1. Results of PC in desalination plant for LSTM.
Training Phase
Testing Phase
MSE
RMSE
MEA
MSE
RMSE
MEA
LSTM-M1
0.3945
0.6281
0.0945
0.3168
0.5628
0.1468
LSTM-M2
0.5444
0.7378
0.0644
0.4284
0.6545
0.1884
Table 1. Results of PC in desalination plant for LSTM.
LSTM-M1
LSTM-M2
Water 2023, 15, 3515
1.0
1.0
0.8
0.8
Probability
Probability
Training Phase
MSE
RMSE
MEA
0.3945
0.6281
0.0945
0.5444
0.7378
0.0644
0.6
0.4
LSTM-M1
Training Phase
0.2
0.4
LSTM-M1
Testing Phase
Observed PV
Simulated PC
0.0
0.0
1.0
0.2
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
1.0
1.0
LSTM-M2
Testing Phase
0.8
0.6
LSTM-M2
Training Phase
0.4
0.2
Probability
0.8
Probability
0.6
0.2
Observed PC
Simulated PC
0.0
Observed PC
Simulated PC
0.6
0.4
0.2
Observed PC
Simulated PC
0.0
0.0
0.0
0.2
0.4
0.6
0.8
1.0
.2
1.0
1.0
0.8
0.8
Probability
Probability
Testing Phase
MSE
RMSE
MEA
11 of 17
0.3168
0.5628
0.1468
0.4284
0.6545
0.1884
0.6
0.4
LSTM-CSA-M1
Training Phase
0.2
Observed PC
Simulated PC
0.0
0.0
0.2
0.4
0.6
Figure 5. Cont.
0.8
1.0
.3
.4
.5
.6
.7
0.6
0.4
LSTM-CSA-M1
Testing Phase
0.2
Observed PC
Simulated PC
0.0
0.2
0.4
0.6
0.8
1.0
1212
of of
17 17
1.0
1.0
0.8
0.8
Probability
Probability
Water
2023,
15, 15,
x FOR
Water
2023,
3515PEER REVIEW
0.6
0.4
LSTM-CSA-M2
Training Phase
0.2
Observed PC
Simulated PC
0.0
0.6
0.4
LSTM-CSA-M2
Testing Phase
0.2
Observed PC
Simulated PC
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
1.0
Figure
(CDF)of
ofPC
PCsimulation.
simulation.
Figure5.5.The
Theprobability
probabilitydistribution
distribution function
function (CDF)
TheCDF
CDFisisaastatistical
statisticalconcept
concept used
used to
to compare
(empirThe
comparethe
thedistribution
distributionofofobserved
observed
(empirical)data
datawith
withthat
that of
of simulated
simulated (model-generated)
into
how
ical)
(model-generated)data.
data.ItItprovides
providesinsights
insights
into
how
closely
the
simulated
data
matches
the
observed
data
in
terms
of
their
distribution
and
closely the simulated data matches the observed data in terms of their distribution and
thelikelihood
likelihoodofofspecific
specific values
values occurring.
occurring. The
hashas
the
The graph
graphdisplayed
displayedthat
thatLSTM-CAS-M2
LSTM-CAS-M2
the highest agreement between the observed and simulated PC. A good match between
the highest agreement between the observed and simulated PC. A good match between
the observed and simulated CDFs suggests that the simulated PC data closely resemble
the observed and simulated CDFs suggests that the simulated PC data closely resemble
the observed data in terms of their distribution. Since the CDFs align well, this indicates
the
observed data in terms of their distribution. Since the CDFs align well, this indicates
that the model’s predictions are consistent with the real-world desalination data. The comthat
the model’s
are consistent
the
real-world
desalination
data. Therisk
comparison
of CDFspredictions
is widely used
in various with
fields,
such
as climate
modeling, financial
parison
of
CDFs
is
widely
used
in
various
fields,
such
as
climate
modeling,
financial
risk
assessment, and quality control. Further numerical comparison of the results is presented
assessment,
and
quality
control.
Further
numerical
comparison
of
the
results
is
presented
using MAE measures. The MAE indicated the average absolute difference between the
using
MAEand
measures.
The MAE
indicated
average
absolute
difference
between
predicted
actual values.
It gives
a sensethe
of the
average
magnitude
of errors
withoutthe
predicted
actual
It gives
a sense
of errors
without
squaring and
them.
Fromvalues.
the training
results
it canof
bethe
seenaverage
that themagnitude
MAE of LSTM-M1
= 0.0945,
the MAE
of LSTM-M2
0.0644, the
MAE
of the
= 0.0399,
and the=MAE
squaring
them.
From the=training
results
it can
be LSTM-CSA-M1
seen that the MAE
of LSTM-M1
0.0945,
ofMAE
the LSTM-CSA-M2
0.0945. the
TheMAE
results
that the LSTM-CSA-M1
the
of LSTM-M2 ==0.0644,
ofshow
the LSTM-CSA-M1
= 0.0399, has
andthe
thelowest
MAE of
MAE
(0.0399), implying
that
it has
the smallest
average
absolute errorhas
in predicting
the
LSTM-CSA-M2
= 0.0945.
The
results
show that
the LSTM-CSA-M1
the lowest PC
MAE
during
the
training
phase
(see
Table
2).
On
the
other
hand,
the
LSTM-CSA-M2
has
the
(0.0399), implying that it has the smallest average absolute error in predicting PC during
lowest
valuephase
for RMSE
that ithand,
is the the
mostLSTM-CSA-M2
accurate model has
in predicting
the
training
(see (0.3804),
Table 2).suggesting
On the other
the lowest
PC
in
the
training
phase
(see
Figure
6).
value for RMSE (0.3804), suggesting that it is the most accurate model in predicting PC in
the training phase (see Figure 6).
Table 2. Results of PC in desalination plant for LSTM-CSA.
Table 2. Results of PC in desalination
plant for
LSTM-CSA.
Training
Phase
MSETraining
RMSE
Phase MEA
LSTM-CSA-M1
LSTM-CSA-M2
LSTM-CSA-M1
LSTM-CSA-M2
0.1664
MSE
0.1447
0.1664
0.1447
0.4079
RMSE
0.3804
0.4079
0.3804
0.0399
MEA
0.0945
0.0399
0.0945
Testing Phase
MSE
RMSEPhaseMEA
Testing
0.1985
0.4456
MSE
RMSE 0.1985
MEA
0.1992
0.4463
0.1292
0.1985
0.4456
0.1985
0.1992
0.4463
0.1292
x FOR PEER REVIEW
Water 2023, 15, 3515
1313of
of 17
MAE-Values for PC (µS/cm)
0.24
0.20
0.16
MAE-Training
MAE-Testing
0.12
0.08
0.04
LSTM-M1
LSTM-M2
LSTM-CSA-M1 LSTM-CSA-M2
Models Combinations
0.70
RMSE-Values PC (µS/cm)
0.65
RMSE-Training
RMSE-Testing
0.60
0.55
0.50
0.45
0.40
0.35
LSTM-M1
LSTM-M2
LSTM-CSA-M1 LSTM-CSA-M2
Figure 6. Error values of PC between the observed and simulated values.
Models Combination
However,
the LSTM-CSA-M2
performs
across values.
all three metrics (MSE, RMSE,
Figure
6. Error values
of PC between the
observedthe
andbest
simulated
and MAE) among the four models during the training phase for PC. The LSTM-CSA-M1
has the
second-best
performance, performs
with the lowest
indicating
the smallest
However,
the LSTM-CSA-M2
the bestMAE
across
all three metrics
(MSE,average
RMSE,
absolute
error.
These
metrics
collectively
offer
insight
into
the
accuracy
and
precision of
and MAE) among the four models during the training phase for PC. The LSTM-CSA-M1
the model’s
predictions,
helping to with
identify
most suitable
predicting
PC
has
the second-best
performance,
thewhich
lowestmodel
MAEisindicating
the for
smallest
average
in the desalination
plant’s
training
phase.offer
In intricate
like desalination,
where
absolute
error. These
metrics
collectively
insight processes
into the accuracy
and precision
of
uncertainties
arise
from
both
human
activities
and
the
characteristics
of
the
source
water,
the model’s predictions, helping to identify which model is most suitable for predicting
the connections among physicochemical factors are prone to being nonlinear due to these
PC in the desalination plant’s training phase. In intricate processes like desalination,
uncertain factors. The evidence in Table 2 indicates that the PC simulation was shown to
where uncertainties arise from both human activities and the characteristics of the source
be a satisfactory and reliable simulation in the testing phase. The quantitative comparison
water, the connections among physicochemical factors are prone to being nonlinear due
of the testing phase depicted that MSE measures the average of the squared differences
to these uncertain factors. The evidence in Table 2 indicates that the PC simulation was
between the predicted and actual values. Lower MSE values indicate that the model’s
shown to be a satisfactory and reliable simulation in the testing phase. The quantitative
Water 2023, 15, x FOR PEER REVIEW
Water 2023, 15, 3515
14 of 17
14 of 17
comparison of the testing phase depicted that MSE measures the average of the squared
differences between the predicted and actual values. Lower MSE values indicate that the
model’s
predictions
aretocloser
to thevalues.
actual values.
In thisthe
case,
the LSTM-CSA-M1
and
predictions
are closer
the actual
In this case,
LSTM-CSA-M1
and LSTMLSTM-CSA-M2
have
the
lowest
MSE
values,
suggesting
that
these
models
have
better
CSA-M2 have the lowest MSE values, suggesting that these models have better overall
overall
prediction
accuracy
in comparison
to the
other models.
The numerical
prediction
accuracy
in comparison
to the other
models.
The numerical
accuracyaccuracy
for each
for
each
model
in
the
testing
phase
was
as
follows:
LSTM-M1
(MSE
=
RMSE
=
model in the testing phase was as follows: LSTM-M1 (MSE = 0.3168, 0.3168,
RMSE =
0.5628,
0.5628,
MEA
=
0.1468),
LSTM-M2
(MSE
=
0.4284,
RMSE
=
0.6545,
MEA
=
0.1884),
the
LSTMMEA = 0.1468), LSTM-M2 (MSE = 0.4284, RMSE = 0.6545, MEA = 0.1884), the LSTM-CSACSA-M1
= 0.1985,
RMSE
= 0.4456,
MEA
0.1985),the
theLSTM-CSA-M2
LSTM-CSA-M2 (MSE
(MSE == 0.1992,
M1 (MSE(MSE
= 0.1985,
RMSE
= 0.4456,
MEA
= =0.1985),
0.1992,
RMSE
=
0.4463,
MEA
=
0.1292).
Similarly,
the
lower
RMSE
values
indicate
better
predictive
RMSE = 0.4463, MEA = 0.1292). Similarly, the lower RMSE values indicate better predictive
performance.
LSTM-CSA-M1and
andLSTM-CSA-M2
LSTM-CSA-M2have
havethe
the
lowest
RMSE
valperformance. Similarly,
Similarly, LSTM-CSA-M1
lowest
RMSE
values,
ues,
implying
that
these
models
are
better
at
minimizing
prediction
errors.
In
this
case,
implying that these models are better at minimizing prediction errors. In this case, the
the
LSTM-CSA-M2
lowest
MEA
value,suggesting
suggestingthat
thatitithas
has the
the smallest
smallest average
LSTM-CSA-M2
hashas
thethe
lowest
MEA
value,
average
prediction
prediction error.
error. Based
Based on
on these
these metrics,
metrics, ititappears
appearsthat
thatthe
themodels
modelswith
withthe
theprefix
prefixLSTMLSTMCSA
CSA (LSTM
(LSTM with
with CSA)
CSA)tend
tendto
toperform
performbetter
betterthan
thanthe
theother
othermodels
models(LSTM
(LSTMwithout
withoutCSA)
CSA)
across
three metrics.
metrics.Additionally,
Additionally,between
betweenthe
theLSTM-CSA-M1
LSTM-CSA-M1
and
LSTM-CSAacross all three
and
thethe
LSTM-CSA-M2,
M2,
the latter
(LSTM-CSA-M2)
seems
to outperform
former
with
slightly
lower
values
the latter
(LSTM-CSA-M2)
seems
to outperform
thethe
former
with
slightly
lower
values
in
in
most
metrics
(see
Figure
7).
most metrics (see Figure 7).
Figure
Figure 7.
7. Fan
Fanplot
plot showing
showing the
the MSE
MSE error
error values
values for
for the
the training
training and
and testing
testing phases.
phases.
4. Conclusions
Conclusions
4.
In the
the face
face of
of ever-growing
ever-growing ecological
ecological challenges
challenges and
and the
the critical
critical importance
importance of
of the
the
In
sustainable
development
goals,
it
is
evident
that
innovative
solutions
are
a
necessity.
This
sustainable development goals, it is evident that innovative solutions are a necessity. This
research highlights
highlights the
in in
advancing
desaliresearch
the transformative
transformativepotential
potentialofofartificial
artificialintelligence
intelligence
advancing
denation
processes,
particularly
in
addressing
the
global
issue
of
water
scarcity.
By
focusing
salination processes, particularly in addressing the global issue of water scarcity. By foon the hybrid
NF–RONF–RO
process,process,
this study
an AI model
deep
learning
LSTM
cusing
on the hybrid
thisintroduces
study introduces
an AIusing
model
using
deep learncombined
with the metaheuristic
CSA, termed
thetermed
LSTM-CSA.
This modelThis
wasmodel
rigorously
ing
LSTM combined
with the metaheuristic
CSA,
the LSTM-CSA.
was
tested
based
on
several
performance
criteria
and
validated
using
both
external
and
internal
rigorously tested based on several performance criteria and validated using both external
validation
a preliminary
a Monte
Carlo
and
internaltechniques,
validation with
techniques,
with a uncertainty
preliminaryassessment
uncertaintyusing
assessment
using
a
simulation.
The
statistical
performance
of
the
models
was
commendable.
The
LSTM
model
Monte Carlo simulation. The statistical performance of the models was commendable. The
displayed
noteworthy
but accuracy,
the LSTM-CSA
outperformed
it, suggesting that
the
LSTM
model
displayedaccuracy,
noteworthy
but the
LSTM-CSA outperformed
it, sugintegration
of
the
CSA
with
deep
learning
augments
predictive
capability.
This
was
further
gesting that the integration of the CSA with deep learning augments predictive capability.
corroborated
viacorroborated
innovative 2D
suchmethods,
as the CDF
This
was further
viagraphical
innovativevisualization
2D graphicalmethods,
visualization
suchand
as
fan plot, which added depth to the accuracy evaluation by accounting for various other
the CDF and fan plot, which added depth to the accuracy evaluation by accounting for
assessment indicators. Beyond just the technical accomplishments, the broader implications
of this research are profound. AI, as demonstrated, can be critical in making desalination
processes more energy-efficient, opening avenues for substantial energy savings. It can
Water 2023, 15, 3515
15 of 17
further guide the development of advanced techniques to treat brine, allowing for resource
extraction and thereby ensuring minimal wastage. In essence, an AI model is not only
reliable promise for enhancing desalination processes but also propels the sector toward
a more sustainable and efficient future. The quantitative summary is presented in the
following points.
•
•
•
•
LSTM-M1: this model has an MSE of 0.3168, an RMSE of 0.5628, and an MEA of 0.1468.
Among the models listed, it performs better than LSTM-M2 but is outperformed by
both LSTM-CSA variants in all three metrics, indicating it has good predictive accuracy
and reliability.
LSTM-M2: This model demonstrates the highest error rates across all three metrics,
with an MSE of 0.4284, RMSE of 0.6545, and MEA of 0.1884, indicating it has the least
predictive accuracy and reliability among the listed models.
LSTM-CSA-M1: this model outperforms the LSTM models in all metrics with an MSE
of 0.1985, RMSE of 0.4456, and MEA of 0.1985. Its error rates are lower, showcasing enhanced predictive accuracy and reliability, substantiating the effectiveness of
integrating the CSA with LSTM.
LSTM-CSA-M2: this model reveals error metrics very close to the LSTM-CSA-M1,
with an MSE of 0.1992, RMSE of 0.4463, and an MEA of 0.1292. It has the lowest MEA
among all models, indicating it has the smallest average prediction error, making it
the most reliable model for predictions among the ones listed.
Author Contributions: Conceptualization, S.I.A. and J.U.; Data curation, N.B.; Funding acquisition,
S.I.A. and J.U.; Investigation, S.I.A., J.U. and D.U.L.; Methodology, J.U.; Project administration,
I.H.A.; Resources, I.H.A.; Software, I.A. and A.G.U.; Supervision, I.H.A.; Validation, D.U.L. and N.B.;
Visualization, S.I.A.; Writing—original draft, J.U. and A.G.U.; Writing—review and editing, I.A. and
A.G.U. All authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by the Deanship of Research Oversight and Coordination (DROC)
at King Fahd University of Petroleum & Minerals (KFUPM) under the Interdisciplinary Research
Center for Membranes and Water Security.
Data Availability Statement: Data are available upon request.
Acknowledgments: Authors would like to acknowledge all support from the Interdisciplinary
Research Center for Membranes and Water Security and that of DROC at King Fahd University of
Petroleum and Minerals.
Conflicts of Interest: The authors declare no conflict of interest.
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